Tuning acoustic impedance in load-bearing structures

Acoustic transparency is the capability of a medium to transmit mechanical waves to adjacent media, without scattering. This characteristic can be achieved by carefully engineering the acoustic impedance of the medium -- a combination of wave speed and density, to match that of the surroundings. Owing to the strong correlation between acoustic wave speed and static stiffness, it is challenging to design acoustically transparent materials in a fluid, while maintaining their high structural rigidity. In this work, we propose a method to design architected lattices with independent control of the elastic wave speed at a chosen frequency, the mass density, and the static stiffness, along a chosen loading direction. We provide a sensitivity analysis to optimize these properties with respect to design parameters of the structure, that include localized masses at specific positions. We demonstrate the method on five different periodic, three dimensional lattices, to calculate bounds on the longitudinal wave speed as a function of their density and stiffness. We then perform experiments on 3-D printed structures, to validate our numerical simulations. The tools developed in this work can be used to design lightweight and stiff materials with optimized acoustic impedance for a plethora of applications, including ultrasound imaging, wave filtering and waveguiding.